Analisis Dinamik Model Matematika Belanja Online Orde Fraksional
Abstract
The growth of online shopping is strongly influenced by information dissemination within society; however, its dynamic behavior has not been fully explored using mathematical approaches. This study aims to analyze the dynamics of online shopping by developing a fractional-order mathematical model that describes the interaction between non-online buyers, online buyers, and information density. The research method employs a literature study and mathematical modeling approach, followed by equilibrium stability analysis and numerical simulations for various fractional orders and information-related parameters. The results indicate the existence of two stable conditions, namely the online shopping-free equilibrium and the endemic online shopping equilibrium. The fractional order significantly affects the speed at which the system reaches equilibrium, while the balance between information generation and decay rates determines the long-term sustainability of online shopping. These findings highlight the crucial role of information in shaping and maintaining online shopping behavior in society.
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